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Hamiltonian structure of 2D fluid dynamics with broken parity

by Gustavo Machado Monteiro, Alexander G. Abanov, Sriram Ganeshan

Submission summary

As Contributors: Gustavo Machado Monteiro
Arxiv Link: (pdf)
Date submitted: 2021-08-17 17:06
Submitted by: Machado Monteiro, Gustavo
Submitted to: SciPost Physics
Academic field: Physics
  • Fluid Dynamics
  • Statistical and Soft Matter Physics
Approach: Theoretical


Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

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Submission 2105.01655v2 on 17 August 2021

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